Is it possible to extract real physical values from multiphase LBM simulation with Shan-Chen force?

Is it possible to extract real physical values from multiphase Lattice Boltzmann method simulation with Shan-Chen force?

SC force is of the form

$$vec{F^{SC}} = -psi(vec{x}) G sum_i w_i psi(vec{x}+vec{c}_iDelta t) vec{c}_i Delta t$$

with pseudopotental $psi(rho)=rho_0(1-exp{(-rho/rho_0)})$ and equation of state

$$p(rho) = c_s^2rho + frac{c_s^2 Delta t^2 G}{2}psi^2(rho)$$
where $c_s$ is the speed of sound.

Also, how does one set a value of $G$ in a simulation? Is it just trial and error until your simulation matches experiment?

For example, I’ve been looking at this simulation of a liquid droplet surrounded by gas phase, which accompanies this book, and tried extracting conversion factors between lattice units and physical ones by looking at kinematic viscosity, delta pressure (laplace pressure) and matching them to real substances (which I guessed). But the derived conversion factors give me ridiculous values when I try to calculate physical density and other quantities.

And now I am questioning whether it’s possible at all, since I am not sure if that $G$ or EOS represent anything real.